Final answer:
When the function f(x) = x is scaled to become g(x) = 3f(x), the slope is tripled, but the y-intercept remains at 0. Changing a line's y-intercept would shift the line up or down without altering the slope.
Step-by-step explanation:
The question is asking about the effect of changing the y-intercept on the graph of a function. According to the provided information, an original line with a y-intercept of 9 and a slope of 3 is described. When the function f(x) = x is multiplied by 3 to get g(x) = 3f(x), the slope is tripled, but the y-intercept does not change because f(x) passes through the origin (0,0) and thus has a y-intercept of 0 to begin with. Therefore, in the example given, the graph of g(x) will have a slope of 3 times the slope of f(x), but the y-intercept will remain the same, at the origin.
If we were to change the y-intercept of a line by some value, the line would shift up or down on the graph, maintaining the same slope. If the y-intercept is increased, the line shifts up; if it is decreased, the line shifts down. This does not affect the steepness or direction of the line, only its vertical position.